AI 中文总结
该研究刻画了单模积性函数沿特定线性分式序列的极限点集，证明其极限集为单位圆有限子群或整个单位圆，推广了Klurman与Mangerel的二分结论。
AI 中文摘要
设a,c为自然数，b,d为整数，且非空集合$R_{a,b,c,d}:=\left\{\frac{an+b}{cn+d}\colon n\in\mathbb{N}\right\} \cap\bigl(\mathbb{Q}_{>0}\setminus\{1\}\bigr)$是积性回归的，我们对所有属于$\mathcal{M}$的单模积性函数f沿$R_{a,b,c,d}$的极限点集给出完整刻画，证明其可能的极限集要么是单位圆的有限子群，要么是整个单位圆，从而推广了Klurman与Mangerel的二分结论。
英文摘要
For $a,c\in\mathbb{N}$ and $b,d\in\mathbb{Z}$ such that the (non-empty) set \[ R_{a,b,c,d} :=\left\{\frac{an+b}{\,cn+d\,}: n\in\mathbb{N}\right\} \cap\bigl(\mathbb{Q}_{>0}\setminus\{1\}\bigr) \] is multiplicatively recurrent, we give a complete characterization of the set of limit points of every unimodular multiplicative function $f\in\mathcal{M}$ along $R_{a,b,c,d}.$ We show that the possible limit sets are either the finite subgroups of the unit circle or the entire circle, thereby extending the dichotomy of Klurman--Mangerel.
Comments12 pages
